Generalized quasi-variational-like inclusions with (a, η) and relaxed cocoercive mappings

Abstract

In this paper, we study an existence theorem of solutions for generalized quasivariational-like inclusions involving (A, η) and relaxed cocoercive mappings. We haveshown that the approximate solutions obtained by proposed algorithm converge tothe exact solutions of generalized quasi-variational-like inclusions. As an application,we have shown that generalized quasi-variational-like inclusions include optimizationproblems and also an equivalence with A-resolvent equations is given.